In what ratio must rice costing Rs 30 per kg be mixed with rice costing Rs 40 per kg so that the mixture costs Rs 34 per kg?

Question

A glass is initially filled entirely with milk. In each step, $\frac{2}{3}$ of the milk is replaced with water. This process is repeated 3 times. What is the final ratio of water to milk in the glass?

Answer 1

Let the ratio be $x : y$. Then $\dfrac{30x + 40y}{x + y} = 34 \Rightarrow 30x + 40y = 34x + 34y \Rightarrow 6y = 4x \Rightarrow \dfrac{x}{y} = \dfrac{3}{2}$, i.e. $3 : 2$.

In what ratio must rice costing Rs 30 per kg be mixed with rice costing Rs 40 per kg so that the mixture costs Rs 34 per kg?

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The Correct Option is B

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